Algebraic groups of homotopy classes of automorphisms and operadic Koszul duality
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916382111694848 |
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| author | Saleh, Bashar |
| author_facet | Saleh, Bashar |
| contents | Given a simply connected space $X$, there are several, a priori different, algebraic groups whose groups of $\mathbb Q$-points are isomorphic to the group of homotopy classes of homotopy automorphisms of the rationalization of $X$. We will show that two of these different algebraic groups are isomorphic using the theory of operadic Koszul duality. As a by-product of the techniques we use, we deduce some isomorphisms of sets of homotopy classes of maps that might be viewed as Eckmann-Hilton dual to some well-known isomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02076 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraic groups of homotopy classes of automorphisms and operadic Koszul duality Saleh, Bashar Algebraic Topology Given a simply connected space $X$, there are several, a priori different, algebraic groups whose groups of $\mathbb Q$-points are isomorphic to the group of homotopy classes of homotopy automorphisms of the rationalization of $X$. We will show that two of these different algebraic groups are isomorphic using the theory of operadic Koszul duality. As a by-product of the techniques we use, we deduce some isomorphisms of sets of homotopy classes of maps that might be viewed as Eckmann-Hilton dual to some well-known isomorphisms. |
| title | Algebraic groups of homotopy classes of automorphisms and operadic Koszul duality |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2305.02076 |